718 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 44, NO. 8, AUGUST 2008 Threshold of a Symmetrically Pumped Distributed Feedback Fiber Laser With a Variable Phase Shift Yuri O. Barmenkov, Alexander V. Kir’yanov, Pere Pérez-Millán, José Luis Cruz, and Miguel V. Andrés, Member, IEEE Abstract—In this paper, we study, both theoretically and exper- imentally, the threshold characteristics of a distributed feedback fiber laser that depend on the value of a phase shift introduced into the fiber Bragg grating structure. We show that as the phase shift possesses a noticeable birefringence, the laser oscillates at any phase shift value. We also reveal that the laser threshold is different for the cavity eigen polarizations and depends on the phase shift value. We derive a simple analytical formula to calculate the laser threshold in the case of phase shift; this formula can be utilized to estimate a minimal threshold value for the laser with certain active fiber and Bragg grating parameters. The developed theory allows us to fairly model the experimen- tally measured dependence of the laser threshold on induced phase shift value. Index Terms—Distributed feedback fiber laser (DFB FL), erbium-doped fiber, laser threshold, polarization state, variable phase shift. I. INTRODUCTION A T PRESENT, distributed feedback (DFB) fiber lasers (FLs) attract much interest owing to their applicability to optical communications, fiber sensors and spectroscopy. DFB FLs are typically single-mode devices that have narrow line width [1], high signal-to-noise ratio [2], and relatively low cost. They have been shown to operate both in the con- tinuous-wave and -switching [3], [4] regimes. A DFB FL is usually implemented by writing, with the use of UV light, a long fiber Bragg grating (FBG) inside a rare-earth-doped fiber, and subsequently introducing a spatial phase shift into the grating. So far, a lot of research has been conducted on DFB FLs towards optimization of their parameters [5], [6], treatment of the cavity’s standing mode profile [7], [8], performance limitations [9], intensity and frequency noise features [2], [10], analysis of the fundamental and higher mode thresholds [11], polarization characteristics [12], etc. Manuscript received July 27, 2007. This work was supported in part by CONACyT Grant 47029, México, and in part by the Ministerio de Educación y Ciencia under Grant TEC2005-07336-C02-01 and Grant PCI2005-A7-0209, Spain. Y. O. Barmenkov and A. V. Kir’yanov are with the Centro de Investigaciones en Optica, 37150 Leon, Mexico (e-mail: yuri@cio.mx; kiryanov@cio.mx). P. Pérez-Millán, J. L. Cruz, and M. V. Andrés are with the Departamento de Física Aplicada—ICMUV, Universidad de Valencia, E46100 Burjassot (Va- lencia), Spain (e-mail: Pere.Perez@uv.es; Jose.L.Cruz@uv.es, miguel.andres@ uv.es). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JQE.2008.923555 Fig. 1. DFB FL structure. FBG1 and FBG2 are two equal phase Bragg grat- ings written in an active fiber and divided by a short-length defect introducing a variable spatial phase shift. The cavity length is taken as a sum of FBGs’ lengths . In the present work, we study, both theoretically and experi- mentally, the threshold characteristics of a DFB FL that are de- pendent on the value of a phase shift introduced into the DFB structure. We show that if the phase shift is notably “birefrin- gent,” i.e., different for two orthogonal polarizations, lasing in the DFB FL can be attainable at any phase shift value, and the laser threshold is different for each of the cavity eigen polar- izations. A simple analytical formula to calculate the threshold of a DFB FL is derived in the case where the phase shift is , which is the minimal threshold value for the laser with certain fiber gain and grating strength. II. EXPERIMENTAL SETUP AND RESULTS In experiments, we studied the threshold characteristics of a DFB FL. The laser was built using the standard procedure [13] of exposing a preliminary hydrogenised Er-doped photosensi- tive fiber to UV-light through a phase mask, thus writing a uni- form FBG in it. A variable phase shift was introduced into the FBG by gluing a central (4-mm) fiber segment to a small rod of magnetostrictive alloy, which in turn was subject to a per- manent magnet field. The phase shift was varied within an in- terval of several ’s by changing the distance between the rod and the magnet. The active fiber (DF1500L-980) had a nonsatu- rated (weak-signal) absorption coefficient cm and a full-saturated gain coefficient cm , both measured at a wavelength of 1532 nm. The DFB cavity length was cm, and the FBG efficiency at Bragg wavelength, nm, was 41.3 dB, yielding a coupling coefficient cm . The FBG written in the active fiber was checked to be uni- form throughout its length. The reflection coefficient of each of the two FBG-halves (FBG1 and FBG2 on Fig. 1), separated by the phase defect, was measured to be the same with high accuracy (the measurements were performed on a slight elongation of the fiber piece containing only one of the FBG halves, what allowed the testing of each part separately). 0018-9197/$25.00 © 2008 IEEE